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Uncertainty exists widely in engineering design. As one of the key components of engineering design, uncertainty propagation and quantification has always been an important research topic. Polynomial chaos (PC) is a highly efficient uncertainty propagation method which has been widely studied and applied. Therefore, this paper reviews recent advances in the PC method. First, the fundamentals of PC are introduced, including the construction of an orthogonal polynomial basis and the calculation of PC coefficients. Second, strategies such as basis truncation, sparse reconstruction, sparse grid and multi-fidelity modeling are described to address the "curse of dimensionality" issue of PC. Local and global sensitivity analyses based on PC are then introduced. Finally, the research prospects of PC are given.